I don't think that it makes sense to see all Western archievements as coming out of the Western analytical mindset. Western society has always been diverse and contained people with different mindsets.
The Greek had steam engines before the invention of the modern scientific method, so I don't see how the modern scientific method was a requirement for the invention of steam engines.
I do grant that the scientific method has important effect on the way our modern technology works, but I think you get into problems when you start to claim that all of our modern technology is due to the scientific method and analytic thinking.
The Greek had steam engines before the invention of the modern scientific method
Actually, you brought the invention of the steam engine into the conversation.
And, while the Greeks invented a rudimentary steam engine, the ancient Greek engine was not really of any practical use. Developing a commercially viable steam engine did not occur until much later. Developing a steam engine that could be used reliably, safely and efficiently for transportation, etc., required scientific knowledge of thermodynamics, behavior of gases, metallurgy, etc.
...I do grant
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